The Ghanaian only arrived at the Liberty Stadium at the start of this season.
"Swansea gave me everything that I wanted, in terms of football and financially. Now, I am ambitious and we will see what happens," he told radio station RMC.
While Garry Monk's men began the campaign strongly - holding Chelsea to a draw at Stamford Bridge on the opening day, before wins against Newcastle and Manchester United followed in their next three games - they have been struggling for form, and have only won once in their last nine.
Despite his team's problems, Ayew has maintained his good form, scoring six times, including an audacious backheel against Bournemouth last weekend.
Meanwhile, the Reds have enjoyed an upturn in their fortunes since Jurgen Klopp arrived at Anfield last month. The Merseyside outfit's loss against Crystal Palace before the international break was the only time that the German has tasted defeat since taking over from former Swans boss Brendan Rodgers.
Should Swansea's woes continue over the Christmas period, while Liverpool continue to impress, then his desire to move on may well increase.